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Chemistry 231. Physical Transformations of Pure Substances. The Definition of a Phase. Phase – a region of system inside which we have uniformity of the chemical potential and physical properties. Three Principal kinds of phases Solid – long-range order Liquid – less long-range order

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chemistry 231

Chemistry 231

Physical Transformations of Pure Substances

the definition of a phase
The Definition of a Phase
  • Phase – a region of system inside which we have uniformity of the chemical potential and physical properties.
  • Three Principal kinds of phases
    • Solid – long-range order
    • Liquid – less long-range order
    • Gas – random molecular distributions
phase transitions
Phase Transitions
  • A phase transition is the spontaneous conversion of one phase into another.
  • Distinguish between
    • Thermodynamic stability – based on chemical potential differences
    • Metastable (kinetic stability) – slow conversion of one phase into another
the criteria for phase equilibrium
The Criteria for Phase Equilibrium

For two phases to be in equilibrium, the chemical potential of the substance in both phases must be equivalent.

the phase rule
The Phase Rule
  • For a single component system


    • F = degrees of freedom
    • P = number of phases
  • For a single component system, with two phases in equilibrium

F = 3-2 = 1

the definition of vapour pressure
The Definition of Vapour Pressure


The pressure of the vapour above the liquid is called the vapour pressure PJ.

Vapour pressures are temperature dependent.

the fundamental equation applied to phase stability
The Fundamental Equation Applied to Phase Stability
  • Applying the definition of the chemical potential

Assume we apply an infinitesimal change in T or P to two phases in equilibrium

displacement of the phase equilibrium
Displacement of the Phase Equilibrium

When a pressure (or temperature) change is applied to an equilibrium system of two phases (point a), the equilibrium is disturbed.

It can be restored by changing the temperature (or pressure) along the boundary to point b.

the clapeyron equation
The Clapeyron Equation

Defining the transition


The slope of any phase boundary can be obtained from the Clapeyron equation

the solid liquid boundary
The Solid-Liquid Boundary

For the fusion transition


We can re-write the Clapeyron equation to include the enthalpy of fusion

the integrated form
The Integrated Form

The dependence of the melting point on the applied pressure is given as follows

a picture of the solid liquid boundary
A Picture of the Solid Liquid Boundary

From the Clapeyron equation, a typical solid-liquid phase boundary slopes steeply upwards.

Most substances increase their melting points behave in this way.

condensed phase vapour transitions
Condensed Phase – Vapour Transitions

For the transition between a condensed phase and the vapour phase


We can re-write the Clapeyron equation to include the enthalpy of the transition

the clausius clapeyron equation
The Clausius-Clapeyron Equation

Using the ideal gas equation

Note – tr represents vapourization

or sublimation.

boiling points
Boiling Points
  • The boiling point is defined as the temperature at which PJ equals Pext.
    • Normal Boiling Point – Pext = 1 atm.
    • Standard Boiling Point – Pext = 1 bar.
  • Boiling points are pressure dependent (see later).
critical points
Critical Points

Critical temperature (Tc) - the temperature above whicha gas cannot be liquefied

Critical pressure (Pc) – the minimum pressure that needs to be applied at Tc to bring about liquefaction.

Supercritical fluid – fluid at or above the Tc value.

a picture of the liquid vapour boundary
A Picture of the Liquid Vapour Boundary

The phase boundary from the plot of the (T,P) equilibrium points.

The liquid vapour phase boundary terminates at the critical point (not shown).

The solid-vapour phase boundary is identical in shape.

dependence of phase stability on pressure temperature changes
Dependence of Phase Stability on Pressure/Temperature Changes

The temperature dependence of the phase stability is related to the numerical value of the molar entropy!

phase stability with pressure
Phase Stability with Pressure

The dependence of the chemical potential with pressure depends on the volume of the phase!

classifying phase transitions
Classifying Phase Transitions

When we classify phase transitions, we must look at the first and second derivatives of the chemical potentials

the ehrenfest classification i
The Ehrenfest Classification (I)
  • A first order transition
    • At least one of the first derivatives of the chemical potential is discontinuous at the transition point.
    • The second derivative of  is a singularity!
the ehrenfest classification ii
The Ehrenfest Classification (II)
  • A second order transition
    • Both of the first derivatives of the chemical potential are continuous at the transition point.
    • One of the second derivatives of  is discontinuous!
the chemical potential functions at phase transitions
The Chemical Potential Functions At Phase Transitions

The changes in thermodynamic properties for a schematic first-order transition.







second order transitions
Second Order Transitions

The changes in thermodynamic properties for a schematic second-order transition.





the lambda transition in helium
The Lambda Transition in Helium

The fluid-superfluid transition in helium (the  transition).

The heat capacity appears to become infinite (first order).

It actually rises smoothly at the transition point, instead of exhibiting a singularity.

melting points and triple points
Melting Points and Triple Points
  • Melting Point – the temperature at which the solid and the liquid phases are in equilibrium.
    • Normal Melting Point – melting temperature at 1 atm pressure.
    • Standard Melting Point – melting temperature at 1 bar pressure.
  • Melting Points are pressure dependent.
phase diagrams
Phase Diagrams

(P,T) regions where the phases are thermodynamically stable.

A phase boundary is a curve in (T,P) space where the  values of the substance in the different phases are equivalent.

triple point
Triple Point


An invariant point where the solid, liquid, and vapour phases are in mutual equilibrium.

the molecular origin of surface tension
The Molecular Origin of Surface Tension
  • Imbalance of intermolecular forces exists at the liquid-air interface
  • gla= the surface tension that exists at the liquid-air interface
capillary action
Capillary Action
  • The tendency of liquids to rise up in narrow tubes - capillary action.
  • Due to the phenomenon of surface tension.
the complication of contact angles
The Complication of Contact Angles
  • The balance of forces that results in a contact angle, c.
  • The contact angle gives information on the ‘wettability’ of a surface.
capillary rise
Capillary Rise
  • The pressure exerted by a column of liquid is balanced by the hydrostatic pressure.
  • This gives us one of the best ways to measure the surface tension of pure liquids and solutions.
meniscus up or down
Meniscus Up or Down??
  • For a wetting liquid, a capillary rise is observed.
  • For a non-wetting liquid, capillary rise is observed capillary wets the
pressure differential across curved interfaces
Pressure Differential Across Curved Interfaces
  • Pressure differential exists across curved interfaces.
  • Due to surface tension forces
enhancement of vapour pressure
Enhancement of Vapour Pressure
  • Vapour pressure enhancement above the surface of spherical droplets.
  • Due to surface tension forces.